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calculus help again :(

A

alphatarget1

Diamond Member
hi all,

i'm trying to find the tangent line of x^2y^2=((y+1)^2)((4-y)^2) at (0,-2)

so i use implicit differentiations and get dx^2y^2=d((y+1)^2)((4-y)^2)

i'm really confused on how and which rules apply here... a couple of pointers would be greatly appreciated!!!
 
I'm not entirely sure where you get that differential from but it's incorrect. Your best bet is to expand the brackets on the right hand side and then differentiate implicitly with respect to x. Use a product rule as well as implicit differentiation on the left hand side as it is a product of two variables.

Once you've got the differential, put in your values for x and y and solve for dy/dx.
 
Originally posted by: kenleung
hi all,

i'm trying to find the tangent line of x^2y^2=((y+1)^2)((4-y)^2) at (0,-2)

so i use implicit differentiations and get dx^2y^2=d((y+1)^2)((4-y)^2)

i'm really confused on how and which rules apply here... a couple of pointers would be greatly appreciated!!!
Click to expand...

Wow. I feel like a dumbass.

I multiplied the whole thing out and did the partial derivatives and everything without even looking at the formula.

Ok, df / dx is equal to :

- Fx
------ , where Fx (should be subscript x, same for y) is the partial derivative of x and same thing for Fy
Fy

Take a look at where the only x term is in the whole formula. Differentiate this and you get 2xy^2. Plug in (0, -2) and you get 0. Since this is the numerator, don't even bother doing the rest of the differentiation. Looking at this would have saved me 5 minutes.

There you go. The derivative @ (0,-2) = 0. Go from there.

-silver
 
Sorry, forgotten everything i learned from Calculus. Even though i got a B+, i knew what i was doing during the semester. 🙂
 
ok so i factored them (took a while)

i got

(dx/dy)=(2xy^3)/(2y^4-6y^3-24y+32) which is 0 anyway and the equation of the tangent line is -2

can anyone confirm this? I've got most of my homework nailed except for this other question:

If x^2+6xy+y^2=8 find y'' by implicit differentiation

i have no idea on this one...

as always, any help is appreciated 🙂
 
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